Black is caught in a connect-and-die. If Black a, White b captures. Otherwise, White captures at a, and is connected to the outside and escapes, thus living (by tsumego convention).
The double atari is wrong here: Black chooses which group to sacrifice, preventing White from connecting and escaping. Note the the bottom row of four is good for at most one eye. After White captures (perforce: if White tries to start making an eye below, Black will capture and White only gets one eye), Black reduces that to no eyes with the double hane:
This shows that White has only the one eye.
See also: